No; I most certainly did not.

I did not refer to Feynman diagrams, and Feynman diagrams are not evaluated at intermediate points as Lyndon appears to suggest. What would be impossible is an interaction described by half that diagram; and there is no such case in any of Feynman's books.

I don't have the book in front of me; but I am familiar with it, and was reading it last week. This is a Feynman diagram; a very handy technique for particle reactions in quantum physics. Here is an on-line reference from Stanford that people may like to refer to, in order to confirm my remarks.

• Lines contained within the diagram are "virtual" particles, and cannot be observed.
• The lines for virtual particles are associated with energy and momentum, and energy and momentum must balance at every vertex; but the virtual particles themselves don't have to satisfy the rules for relating energy, momentum and rest mass for real particles.
• The lines for particles leaving the diagram do have to satisfy the rules relating energy, momentum and rest mass for real particles.
• A physical real world process is actually described by a sum of many such diagrams; not one diagram. There are many diagrams required for proper analysis of the Compton effect.
• The diagrams are essentially a calculation method; not a description of a simple sequence of events.

If Lyndon wants to use Feynman diagrams to explain his process, that would be great! But they have their own rules as well. If Lyndon does not use Feynman diagrams, then all of this is another red herring. We could spend a few more pages pointing out what a Feynman diagram represents, and how energy momentum is applied to such diagrams, and why it is incorrect to think of midpoints in the diagram representing observable states that might impact on other particles outside the diagram, and so on; and we would still be no nearer having a proper energy momentum analysis for Lyndon's process.

Lyndon proposes not a Compton scattering reaction; but a photo-absorption, in which the electron absorbs a photon, and then is subsequently decelerated within the plasma to emit a CMB photon, and then emits a redshifted photon along the same line as the initial photon, and then is decelerated again to emit another CMB photon.

The initial photo-absorption gives a small boost to an electron to match the initial momentum, and gives energy of Q^2/2mc^2 to the electron. This leaves most of the energy unaccounted for. This is not analogous to virtual particles in the middle of a Feynman diagram, and my arguments don't carry over to virtual particles in the middle of a Feynman diagram. To even make the comparison is yet another error in basic physics, this time in understanding Feynman diagrams.

What Lyndon requires is a plain description of his own process, considering both momentum and energy. If Lyndon wants to invoke intermediate stages in which energy and momentum are not able to be balanced, then he needs to get into quantum physics. For example, I would be fine with a balanced energy momentum analysis, in which there was a very short intermediate state in which the balance is lost. The maximum duration of such stages is given by Heisenberg's Uncertainty Principle.

For example, he could use ΔEΔt <= h/4pi. The description in Lyndon's paper of an electron absorbing a 500nm photon has an energy imbalance of about 4e-19 J, and h/4pi is about 5e-35. The time gap before balance must be restored with the re-emitted photon and the two CMB photons is no more than:
Δt <= h/4piΔE = 1.25e-16 seconds

At different times, Lyndon has proposed a number of possible solutions, all of which would fail to pass review in any credible science journal.

• Lyndon has suggested that the energy is maintained in an excited state of the electron. Unfortunately, there is no such thing.
• Lyndon has suggested oscillations of the electron. As we saw in the example of three electrons and two nails, this tends to violate momentum conservation.
• Lyndon has suggested that the energy ends up in the rest of the plasma. No mechanism for this has been given; and it has the additional problem of getting all the energy back to power re-emission of the electron.
• Lyndon has suggested that the "rest of the universe" can account for the balance. This is pretty much the same as the "rest of the plasma". This should be quantified, with forces and mechanisms identified. Unfortunately, this approach works very poorly for making up an energy imbalance. With very stiff forces as in a rigid crystal lattice, it can be possible to make up momentum imbalance; but energy is invariably ends up mostly in the light weight particles of the immediate reaction.
• This latest post seems to suggest that a temporary imbalance in energy occurs. There is a strong limit of the duration of any such imbalance, by Heisenberg's uncertainty principle, which means there can be no more than about 1.25e-16 seconds before re-emission. This is inconsistent with Lyndon's paper in which an electron has time between absorption and emission to decelerate under the influence of forces in the plasma and emit the CMB photon as bremsstrahlung.

The real problem is that Lyndon fails to pick an approach and stick to it, and never gives a quantified description of any of them sufficient to show consistency with energy momentum conservation.

The solution of having everything happening as part of the one interaction is essentially what I proposed in my analysis a couple of pages back, here.

Cheers -- Sylas